Existing multi-stage clustering methods independently learn the salient features from multiple views and then perform the clustering task. Particularly, multi-view clustering (MVC) has attracted a lot of attention in multi-view or multi-modal scenarios. MVC aims at exploring common semantics and pseudo-labels from multiple views and clustering in a self-supervised manner. However, limited by noisy data and inadequate feature learning, such a clustering paradigm generates overconfident pseudo-labels that mis-guide the model to produce inaccurate predictions. Therefore, it is desirable to have a method that can correct this pseudo-label mistraction in multi-stage clustering to avoid the bias accumulation. To alleviate the effect of overconfident pseudo-labels and improve the generalization ability of the model, this paper proposes a novel multi-stage deep MVC framework where multi-view self-distillation (DistilMVC) is introduced to distill dark knowledge of label distribution. Specifically, in the feature subspace at different hierarchies, we explore the common semantics of multiple views through contrastive learning and obtain pseudo-labels by maximizing the mutual information between views. Additionally, a teacher network is responsible for distilling pseudo-labels into dark knowledge, supervising the student network and improving its predictive capabilities to enhance the robustness. Extensive experiments on real-world multi-view datasets show that our method has better clustering performance than state-of-the-art methods.